Dilation (mathematics)

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In mathematics, a dilation is a function f from a metric space into itself that satisfies the identity

d(f(x),f(y)) = rd(x,y)

where d(x,y) is the distance from x to y and r is some positive real number.

Dilation is yet another name for similarity of a Euclidean space.

Another way to look at a dilation is as a transformation that changes the size but not the shape of an object or figure. Every dilation that is not a congruence has a fixed point that is called the center of dilation.

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